function XK = kesler_construction(X, labels)
% KESLER_CONSTRUCTION - Given a data set returns the Kesler constructed data set for training a multiclass perceptron with
%
% Written by:
% -- 
% John L. Weatherwax                2005-08-04
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

[N,p] = size(X); 

uLabels  = unique(labels);
M        = length(uLabels);

% This ensures that that the class labels are given 1:M i.e. sequentially.
% if they are not this code will create one based labels
%
oneIndexedLabels = zeros(1,N);
for mi=1:M
  inds = find( labels == uLabels(mi) );
  oneIndexedLabels(inds) = mi; 
end

X_Kesler = zeros(N*(M-1),p*M);
xk_spot  = 1; 
for xii=1:N,
  x  = X(xii,:); % get this sample 
  xl = oneIndexedLabels(xii); % get this samples label 
  for jj=1:M,
    if( jj==xl ) 
      continue; 
    end
    xk_sample = zeros(1,p*M); % one Kesler sample 
    xk_sample(1, (p*(xl-1)+1) : (p*xl) ) = +x;
    xk_sample(1, (p*(jj-1)+1) : (p*jj))  = -x;

    X_Kesler(xk_spot,:) = xk_sample;
    xk_spot = xk_spot + 1; 
  end
end

XK = X_Kesler;